There is also good agreement in our distance determinations for \(\omega \)  Cen. The literature distances lead to an average distance of \(D=5.47 \pm 0.06\)  kpc (see Fig. REF ). The Gaia kinematic distance is
in good agreement with the literature distance, however the HST kinematic distance (\(5.26 \pm 0.12\)  kpc) is about 200 pc shorter.
One possible reason for the mismatch could be the intrinsic flattening of \(\omega \)  Cen. [1]} find
an ellipticity of \(\epsilon =0.17\)  for \(\omega \)  Cen based on its projected isophotes. The true flattening is likely even larger, with the exact value depending on the cluster inclination. [2]}
found through axisymmetric Schwarzschild modeling that the resulting flattening of the velocity ellipsoid can decrease the kinematic cluster distance to \(\omega \)  Cen by several hundred pc if the flattening is not
taken into account in the modeling. Since the \(N\) -body models that we use to derive the kinematic distances are spherically symmetric, there is a chance that our kinematic distances underestimate the true distance
to \(\omega \)  Cen. This effect is much less likely for most other clusters which have much smaller relaxation times and should therefore be closer to being spherically symmetric. This is indeed also seen in observations
[3]}. We therefore regard the literature distance as more reliable for \(\omega \)  Cen. The Gaia EDR3 parallaxes after application of the systematic parallax offset
also favor a longer distance, however the error bar is too large to be decide between the two possibilities.
